Eventually you learn to recognise the hand positions almost like they're symbols in their own right. You can tell the difference between an apostrophe and a comma, right? And in certain typefaces they're identical symbols other than their position.

For the same reason, you can tell the difference between an hour hand just past the 12 and an hour hand just past the 6. Then you learn what the other positions look like.

Then you can read the minute hand to whatever precision you need.

After that it's just practise, practise, practise. Your read times will tumble and before long you'll be completely used to it and be just as fast as with digital.